Lychees don't need chill hours in the same way that temperate fruit trees do. It would be more appropriate perhaps to call what lychees need as "stress hours". Different things can provide lychees with needed stress to flower:1) cold, as in night time temperatures below 55F (chill hours for temperate trees are much lower: below 45F), 2)dry spells, or turning off irrigation system to mimic droughts, 3) girdling or cincturing cuts, to cut off flow of carbohydrates to the limbs.
Different cultivars have different requirements, and some are adapted to tropics need little or no stress in order to flower and fruit. For example, Kaimana and B-3 will fruit here where temperatures almost never drop below 60F and where we have no dry spells. No Mai Tze on other hand will not fruit here as it never gets cold enough to trigger flowering.